Rinse the black beans thoroughly under cold water to remove excess salt and canning liquid. Drain well and transfer to a large mixing bowl.
Slice the red onion into small, uniform pieces about 1/4 inch dice. Place the sliced onion in cold water and let it soak for 10 minutes to mellow the sharpness, then drain thoroughly.
Halve or quarter the cherry tomatoes, depending on their size, and add them to the bowl with the beans.
Juice fresh limes until you have about 2 tablespoons of lime juice. Pour the juice into a small bowl for easy mixing.
Add the drained, soaked onions to the bowl with beans and tomatoes. Drizzle the olive oil over the mixture.
Sprinkle ground cumin and smoked paprika over the ingredients, then pour in the lime juice. Gently toss everything together with a mixing spoon until well coated.
Chop the cilantro finely and add it to the bowl. Season with salt and pepper to taste, then toss again to distribute evenly.
Let the salad sit at room temperature for at least 15 minutes to allow flavors to meld. For a deeper flavor, refrigerate for up to 2 hours.
Give the salad a gentle toss just before serving. Taste and adjust seasoning if needed, adding more lime juice or salt for brightness.
Serve the colorful, messy salad in bowls or on a platter, garnished with extra cilantro if desired. Enjoy it chilled or at room temperature for a nostalgic summer treat.